Departments of Applied Mathematics and Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Phys Rev Lett. 2009 Dec 4;103(23):231301. doi: 10.1103/PhysRevLett.103.231301. Epub 2009 Dec 3.
Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can. It has been shown that the amplitudes phi(x(n)) that a field takes at a generic discrete set of points x(n) can be sufficient to reconstruct the field phi(x) for all x, namely, if there exists a certain type of natural ultraviolet (UV) cutoff in nature, and if the average spacing of the sample points is at the UV-cutoff scale. Here, we generalize this information-theoretic framework to spacetimes themselves. We show that samples taken at a generic discrete set of points of a Euclidean-signature spacetime can allow one to reconstruct the shape of that spacetime everywhere, down to the cutoff scale. The resulting methods could be useful in various approaches to quantum gravity.
时空中的场可以是离散和连续的，就像信息一样。已经表明，场在一般离散点集 x(n) 处取的幅度 phi(x(n)) 足以重建所有 x 处的场 phi(x)，即如果自然界存在某种类型的自然紫外 (UV) 截止，并且如果样本点的平均间距处于 UV 截止尺度。在这里，我们将这个信息论框架推广到时空本身。我们表明，在欧几里得时空的一般离散点集上采样，可以允许人们在截止尺度内重建那个时空的形状。由此产生的方法在各种量子引力方法中可能有用。
